SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
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In many cases, the overriding difficulty associated with finite element analyses of complex structures is the generation of error-free finite element meshes. In view of this situation, a number of mesh generation schemes for planar (e.g., [1], [2]) and shell (e.g., [3], [4]) structures have recently been proposed (see [5] for an extensive bibliography). At one extreme are the fully automatic methods in which the computer is used to determine regions of high and low element densities and then create a finite element mesh accordingly. At the other extreme are methods which require the analyst to completely define the element mesh, while the mesh generating algorithm itself performs only minor clerical tasks such as checking for consistency and error detection. While the fully automatic methods tend to be somewhat inflexible and frequently time consuming to implement, the simplest schemes fail to relieve the user of enough of the tedium accompanying manual decomposition of the structure. We feel that the two semi-automatic mesh generation approaches described in this paper offer a good compromise between the two extremes in mesh generation:(i) A semi-automatic mesh generation algorithm capable of generating meshes of triangular elements for the decomposition of any multiply connected, polygonal, planar region. Once the user has described the boundary of the region and supplied any necessary element density input information, the algorithm automatically positions nodes within the region and assembles triangular elements from these nodes.(ii) An interactive method which permits finite element modeling of three-dimenslonal shell structures on a graphic console. The salient features of this approach involve mathematical surfacing techniques which allow a shell to be represented as a mathematically deformed rectangular domain.